Xu GPS

Theory, Algorithms and Applications
3rd Auflage 2016
ISBN: 978-3-662-50367-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 508 Seiten

This reference and handbook describes theory, algorithms and applications of the Global Positioning System (GPS/Glonass/Galileo/Compass). It is primarily based on source-code descriptions of the KSGsoft program developed at the GFZ in Potsdam. The theory and algorithms are extended and verified for a new development of a multi-functional GPS/Galileo software. Besides the concepts such as the unified GPS data processing method, the diagonalisation algorithm, the adaptive Kalman filter, the general ambiguity search criteria, and the algebraic solution of variation equation reported in the first edition, the equivalence theorem of the GPS algorithms, the independent parameterisation method, and the alternative solar radiation model reported in the second edition, the modernisation of the GNSS system, the new development of the theory and algorithms, and research in broad applications are supplemented in this new edition. Mathematically rigorous, the book begins with the introduction, the basics of coordinate and time systems and satellite orbits, as well as GPS observables, and deals with topics such as physical influences, observation equations and their parameterisation, adjustment and filtering, ambiguity resolution, software development and data processing and the determination of perturbed orbits.

Autoren/Hrsg.

Xu, Guochang

Xu, Yan

Inhaltsverzeichnis

1;Preface to the Third Edition;6
1.1;References;9
2;Preface to the Second Edition;10
3;Preface to the First Edition;13
4;Contents;17
5;Abbreviations and Constants;24
5.1;Abbreviations;24
6;1 Introduction;28
6.1;1.1 A Key Note on GPS;29
6.1.1;1.1.1 GPS Modernization;31
6.2;1.2 A Brief Message About GLONASS;34
6.2.1;1.2.1 The Development of GLONASS;34
6.3;1.3 Basic Information on Galileo;36
6.3.1;1.3.1 The Development of Galileo;37
6.4;1.4 Introduction of BeiDou;38
6.4.1;1.4.1 The Development of BeiDou;39
6.5;1.5 A Combined Global Navigation Satellite System;40
6.6;References;41
7;2 Coordinate and Time Systems;43
7.1;2.1 Geocentric Earth-Fixed Coordinate Systems;43
7.2;2.2 Coordinate System Transformations;47
7.3;2.3 Local Coordinate System;48
7.4;2.4 Earth-Centred Inertial Coordinate System;50
7.5;2.5 IAU 2000 Framework;54
7.6;2.6 Geocentric Ecliptic Inertial Coordinate System;58
7.7;2.7 Time Systems;59
7.8;References;62
8;3 Satellite Orbits;63
8.1;3.1 Keplerian Motion;63
8.1.1;3.1.1 Satellite Motion in the Orbital Plane;66
8.1.2;3.1.2 Keplerian Equation;70
8.1.3;3.1.3 State Vector of the Satellite;72
8.2;3.2 Disturbed Satellite Motion;75
8.3;3.3 GPS Broadcast Ephemerides;75
8.4;3.4 IGS Precise Ephemerides;77
8.5;3.5 GLONASS Ephemerides;78
8.6;3.6 Galileo Ephemerides;79
8.7;3.7 BDS Ephemerides;79
8.8;References;79
9;4 GPS Observables;80
9.1;4.1 Code Pseudoranges;80
9.2;4.2 Carrier Phases;82
9.3;4.3 Doppler Measurements;84
9.4;References;86
10;5 Physical Influences of GPS Surveying;87
10.1;5.1 Ionospheric Effects;87
10.1.1;5.1.1 Code Delay and Phase Advance;87
10.1.2;5.1.2 Elimination of Ionospheric Effects;90
10.1.3;5.1.3 Ionospheric Models;93
10.1.4;5.1.4 Mapping Functions;97
10.1.5;5.1.5 Introduction of Commonly Used Ionospheric Models;100
10.2;5.2 Tropospheric Effects;104
10.2.1;5.2.1 Tropospheric Models;105
10.2.2;5.2.2 Mapping Functions and Parameterisation;109
10.2.3;5.2.3 Introduction of Commonly Used Tropospheric Models;112
10.2.4;5.2.4 Tropospheric Model for Airborne Kinematic Positioning;115
10.2.5;5.2.5 Water Vapour Research with Ground-Based GPS Measurement;117
10.3;5.3 Relativistic Effects;118
10.3.1;5.3.1 Special Relativity and General Relativity;118
10.3.2;5.3.2 Relativistic Effects on GPS;121
10.4;5.4 Earth Tide and Ocean Loading Tide Corrections;123
10.4.1;5.4.1 Earth Tide Displacements of GPS Stations;123
10.4.2;5.4.2 Simplified Model of Earth Tide Displacements;125
10.4.3;5.4.3 Numerical Examples of Earth Tide Effects;127
10.4.4;5.4.4 Ocean Loading Tide Displacement;129
10.4.5;5.4.5 Computation of the Ocean Loading Tide Displacement;132
10.4.6;5.4.6 Numerical Examples of Loading Tide Effects;133
10.5;5.5 Clock Errors;134
10.5.1;5.5.1 Introduction of Commonly Used Clock Error Models;136
10.5.2;5.5.2 Impact of Frequency Reference of a GPS Receiver on the Positioning Accuracy;138
10.6;5.6 Multipath Effects;139
10.6.1;5.6.1 GPS Altimetry, Signals Reflected from the Earth’s Surface;141
10.6.2;5.6.2 Reflecting Point Positioning;141
10.6.3;5.6.3 Image Point and Reflecting Surface Determination;143
10.6.4;5.6.4 Research Activities in GPS Altimetry;144
10.7;5.7 Anti-spoofing and Selective Availability Effects;145
10.8;5.8 Antenna Phase Centre Offset and Variation;146
10.9;5.9 Instrumental Biases;150
10.10;References;151
11;6 GPS Observation Equations and Equivalence Properties;157
11.1;6.1 General Mathematical Models of GPS Observations;157
11.2;6.2 Linearisation of the Observation Model;159
11.3;6.3 Partial Derivatives of Observation Function;161
11.4;6.4 Linear Transformation and Covariance Propagation;165
11.5;6.5 Data Combinations;166
11.5.1;6.5.1 Ionosphere-Free Combinations;168
11.5.2;6.5.2 Geometry-Free Combinations;169
11.5.3;6.5.3 Standard Phase–Code Combination;172
11.5.4;6.5.4 Ionospheric Residuals;173
11.5.5;6.5.5 Differential Doppler and Doppler Integration;174
11.6;6.6 Data Differentiations;176
11.6.1;6.6.1 Single Differences;177
11.6.2;6.6.2 Double Differences;180
11.6.3;6.6.3 Triple Differences;182
11.7;6.7 Equivalence of the Uncombined and Combining Algorithms;184
11.7.1;6.7.1 Uncombined GPS Data Processing Algorithms;185
11.7.2;6.7.2 Combining Algorithms of GPS Data Processing;187
11.7.3;6.7.3 Secondary GPS Data Processing Algorithms;192
11.7.4;6.7.4 Summary;195
11.8;6.8 Equivalence of Undifferenced and Differencing Algorithms;196
11.8.1;6.8.1 Introduction;196
11.8.2;6.8.2 Formation of Equivalent Observation Equations;197
11.8.3;6.8.3 Equivalent Equations of Single Differences;199
11.8.4;6.8.4 Equivalent Equations of Double Differences;203
11.8.5;6.8.5 Equivalent Equations of Triple Differences;205
11.8.6;6.8.6 Method of Dealing with the Reference Parameters;206
11.8.7;6.8.7 Summary of the Unified Equivalent Algorithm;207
11.9;References;208
12;7 Adjustment and Filtering Methods;210
12.1;7.1 Introduction;210
12.2;7.2 Least Squares Adjustment;210
12.2.1;7.2.1 Least Squares Adjustment with Sequential Observation Groups;212
12.3;7.3 Sequential Least Squares Adjustment;214
12.4;7.4 Conditional Least Squares Adjustment;216
12.4.1;7.4.1 Sequential Application of Conditional Least Squares Adjustment;218
12.5;7.5 Block-Wise Least Squares Adjustment;219
12.5.1;7.5.1 Sequential Solution of Block-Wise Least Squares Adjustment;221
12.5.2;7.5.2 Block-Wise Least Squares for Code–Phase Combination;223
12.6;7.6 Zhou’s Theory: Equivalently Eliminated Observation Equation System;224
12.6.1;7.6.1 Zhou–Xu’s Theory: Diagonalised Normal Equation and the Equivalent Observation Equation;227
12.7;7.7 Kalman Filter;229
12.7.1;7.7.1 Classic Kalman Filter;229
12.7.2;7.7.2 Kalman Filter: A General Form of Sequential Least Squares Adjustment;231
12.7.3;7.7.3 Robust Kalman Filter;232
12.7.4;7.7.4 Yang’s Filter: Adaptively Robust Kalman Filtering;235
12.7.5;7.7.5 Progress in Adaptively Robust Filter Theory and Application;239
12.7.6;7.7.6 A Brief Introduction to the Intelligent Kalman Filter;241
12.8;7.8 A Priori Constrained Least Squares Adjustment;241
12.8.1;7.8.1 A Priori Parameter Constraints;242
12.8.2;7.8.2 A Priori Datum;243
12.8.3;7.8.3 Zhou’s Theory: Quasi-Stable Datum;245
12.9;7.9 Summary;247
12.10;References;249
13;8 Cycle Slip Detection and Ambiguity Resolution;252
13.1;8.1 Cycle Slip Detection;252
13.2;8.2 Method of Dealing with Cycle Slips;254
13.3;8.3 A General Criterion of Integer Ambiguity Search;254
13.3.1;8.3.1 Introduction;254
13.3.2;8.3.2 Summary of Conditional Least Squares Adjustment;255
13.3.3;8.3.3 Float Solution;257
13.3.4;8.3.4 Integer Ambiguity Search in Ambiguity Domain;258
13.3.5;8.3.5 Integer Ambiguity Search in Coordinate and Ambiguity Domains;259
13.3.6;8.3.6 Properties of Xu’s General Criterion;261
13.3.7;8.3.7 An Equivalent Ambiguity Search Criterion and Its Properties;262
13.3.8;8.3.8 Numerical Examples of the Equivalent Criterion;265
13.3.9;8.3.9 Conclusions and Comments;267
13.4;8.4 Ambiguity Resolution Approach Based on the General Criterion;268
13.5;8.5 Ambiguity Function;270
13.5.1;8.5.1 Xu’s Conjecture: Maximum Property of Ambiguity Function;271
13.6;8.6 Ionosphere-Free Ambiguity Fixing;274
13.6.1;8.6.1 Introduction;274
13.6.2;8.6.2 Concept of Ionospheric Ambiguity Correction;276
13.6.3;8.6.3 Determination of the Ionospheric Ambiguity Correction;279
13.6.4;8.6.4 Integer Ambiguity Fixing Through Ambiguity-Ionospheric Equations;280
13.6.5;8.6.5 Float Ambiguity Fixing;280
13.7;8.7 PPP Ambiguity Fixing;280
13.8;References;282
14;9 Parameterisation and Algorithms of GPS Data Processing;285
14.1;9.1 Parameterisation of the GPS Observation Model;285
14.1.1;9.1.1 Evidence of the Parameterisation Problem of the Undifferenced Observation Model;286
14.1.2;9.1.2 A Method of Uncorrelated Bias Parameterisation;287
14.1.3;9.1.3 Geometry-Free Illustration;293
14.1.4;9.1.4 Correlation Analysis in the Case of Phase–Code Combinations;294
14.1.5;9.1.5 Conclusions and Comments;295
14.2;9.2 Equivalence of the GPS Data Processing Algorithms;296
14.2.1;9.2.1 Equivalence Theorem of GPS Data Processing Algorithms;297
14.2.2;9.2.2 Optimal Baseline Network Forming and Data Condition;299
14.2.3;9.2.3 Algorithms Using Secondary GPS Observables;301
14.2.4;9.2.4 Simplified Equivalent Representation of GPS Observation Equations;302
14.3;9.3 Non-equivalent Algorithms;309
14.4;9.4 Reference Changing in GPS Difference Algorithm;309
14.4.1;9.4.1 Changing Reference Satellite;309
14.4.2;9.4.2 Changing Reference Station;310
14.5;9.5 Standard Algorithms of GPS Data Processing;313
14.5.1;9.5.1 Preparation of GPS Data Processing;313
14.5.2;9.5.2 Single Point Positioning;314
14.5.3;9.5.3 Standard Un-differential GPS Data Processing;319
14.5.4;9.5.4 Equivalent Method of GPS Data Processing;322
14.5.5;9.5.5 Relative Positioning;323
14.5.6;9.5.6 Velocity Determination;324
14.5.7;9.5.7 Kalman Filtering Using Velocity Information;327
14.6;9.6 Accuracy of the Observational Geometry;328
14.7;9.7 Introduction to the Real-Time Positioning System;330
14.7.1;9.7.1 Network RTK;330
14.7.2;9.7.2 PPP-RTK;333
14.8;References;333
15;10 Applications of GPS Theory and Algorithms;335
15.1;10 Applications of GPS Theory and Algorithms;335
15.1.1;10.1.1 Functional Library;335
15.1.2;10.1.2 Data Platform;340
15.1.3;10.1.3 A Data Processing Core;342
15.2;10.1.3 A Data Processing Core;343
15.3;10.1.3 A Data Processing Core;345
15.3.1;10.3.1 Introduction;346
15.3.2;10.3.2 Concept of Precise Kinematic Positioning;348
15.3.2.1;10.3.2.1 Combining the Static References with IGS Station;348
15.3.2.2;10.3.2.2 Earth Tide and Loading Tide Corrections;348
15.3.2.3;10.3.2.3 Multiple Static References for Kinematic Positioning;349
15.3.2.4;10.3.2.4 Introducing Height Information as a Condition;351
15.3.2.5;10.3.2.5 Creation of a Kinematic Tropospheric Model;351
15.3.2.6;10.3.2.6 Higher-Order Ionospheric Effect Correction;352
15.3.2.7;10.3.2.7 A General Method of Integer Ambiguity Fixing;352
15.3.3;10.3.3 Concept of Flight-State Monitoring;352
15.3.4;10.3.4 Results, Precision Estimation, and Comparisons;355
15.3.4.1;10.3.4.1 Multiple Static References for Kinematic Positioning;357
15.3.4.2;10.3.4.2 Ambiguity of Multiple Static References as a Condition for Kinematic Positioning;357
15.3.4.3;10.3.4.3 Multiple Kinematic GPS for Flight-State Monitoring and Its Comparison with INS;359
15.3.4.4;10.3.4.4 Static GPS Data Kinematic Processing;360
15.3.4.5;10.3.4.5 Doppler Velocity Comparisons;360
15.3.5;10.3.5 Conclusions;360
15.4;References;361
16;11 Perturbed Orbit and Its Determination;363
16.1;11.1 Perturbed Equation of Satellite Motion;363
16.1.1;11.1.1 Lagrangian Perturbed Equation of Satellite Motion;364
16.1.2;11.1.2 Gaussian Perturbed Equation of Satellite Motion;367
16.2;11.2 Perturbation Forces of Satellite Motion;370
16.2.1;11.2.1 Perturbation of the Earth’s Gravitational Field;370
16.2.1.1;11.2.1.1 The Earth’s Gravitational Field;370
16.2.1.2;11.2.1.2 Perturbation Force of the Earth’s Gravitational Field;373
16.2.2;11.2.2 Perturbations of the Sun, the Moon, and the Planets;375
16.2.3;11.2.3 Earth Tide and Ocean Tide Perturbations;376
16.2.4;11.2.4 Solar Radiation Pressure;380
16.2.5;11.2.5 Atmospheric Drag;384
16.2.6;11.2.6 Additional Perturbations;387
16.2.7;11.2.7 Order Estimations of Perturbations;389
16.2.8;11.2.8 Ephemerides of the Moon, the Sun, and Planets;390
16.3;11.3 Analysis Solution of the \overline{C}_{20} Perturbed Orbit;394
16.4;11.4 Orbit Correction;401
16.5;11.5 Principle of GPS Precise Orbit Determination;405
16.5.1;11.5.1 Xu’s Algebraic Solution to the Variation Equation;407
16.6;11.6 Numerical Integration and Interpolation Algorithms;409
16.6.1;11.6.1 Runge–Kutta Algorithm;409
16.6.2;11.6.2 Adams Algorithms;413
16.6.3;11.6.3 Cowell Algorithms;416
16.6.4;11.6.4 Mixed Algorithms and Discussions;418
16.6.5;11.6.5 Interpolation Algorithms;419
16.7;11.7 Orbit-Related Partial Derivatives;420
16.8;References;429
17;12 Singularity-Free Orbit Theory;431
17.1;12.1 A Brief Historical Review of the Singularity Problem;431
17.2;12.2 On the Singularity Problem in Orbital Mechanics;434
17.2.1;12.2.1 Basic Lagrangian and Gaussian Equations of Motion;434
17.2.2;12.2.2 Solving Algorithm for the Singularity Problem;439
17.2.3;12.2.3 Xu’s Criteria for Singularity;440
17.2.4;12.2.4 Derivation of Lagrange-Xu Equations of Motion;441
17.2.5;12.2.5 Derivation of Gauss Equations from Lagrange Equations;451
17.2.6;12.2.6 Derivation of Gauss-Xu Equations of Motion;453
17.3;12.3 Bridge Between Analytical Theory and Numerical Integration;456
17.4;References;457
18;13 Discussions;460
18.1;13.1 Independent Parameterisation and A Priori Information;460
18.2;13.2 Equivalence of the GPS Data Processing Algorithms;462
18.3;13.3 Other Comments;463
19;Appendix A: IAU 1980 Theory of Nutation;465
20;Appendix B: Numerical Examples of the Diagonalisation of the Equations;469
21;References;475
22;Index;502